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Topological triviality of deformations of regular mappings
Bulletin des Sciences Mathématiques ( IF 1.3 ) Pub Date : 2020-05-12 , DOI: 10.1016/j.bulsci.2020.102870 Beata Osińska-Ulrych , Tomasz Rodak , Grzegorz Skalski , Stanisław Spodzieja
中文翻译:
正则映射变形的拓扑琐碎性
更新日期:2020-05-12
Bulletin des Sciences Mathématiques ( IF 1.3 ) Pub Date : 2020-05-12 , DOI: 10.1016/j.bulsci.2020.102870 Beata Osińska-Ulrych , Tomasz Rodak , Grzegorz Skalski , Stanisław Spodzieja
We give a sufficient condition for topological triviality of , for mappings , , in terms of the Hörmander-Łojasiewicz inequality , , where Z is the set of critical points of f and ν is the Rabier function. We apply this condition for regular mappings. As a corollary we obtain an estimation of the degree of sufficiency of non-isolated regular mappings' singularities in terms of degrees of polynomials describing the regular mappings.
中文翻译:
正则映射变形的拓扑琐碎性
我们给出了拓扑的琐碎性的充分条件 , 对于 映射 , ,根据Hörmander-Łojasiewicz不等式 , 其中ž是该组的临界点的˚F和ν是Rabier功能。我们将此条件应用于常规映射。作为推论,我们根据描述正则映射的多项式的阶数来估计非隔离正则映射的奇异性的充分程度。